A328194 Maximum length of a divisibility chain of consecutive nontrivial divisors of n (greater than 1 and less than n).

0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 1, 0, 1, 1, 3, 0, 2, 0, 2, 1, 1, 0, 1, 1, 1, 2, 2, 0, 1, 0, 4, 1, 1, 1, 1, 0, 1, 1, 2, 0, 2, 0, 2, 1, 1, 0, 1, 1, 2, 1, 2, 0, 2, 1, 2, 1, 1, 0, 1, 0, 1, 1, 5, 1, 2, 0, 2, 1, 1, 0, 1, 0, 1, 2, 2, 1, 2, 0, 2, 3, 1, 0, 1, 1, 1, 1, 3, 0, 1, 1, 2, 1, 1, 1, 1, 0, 2, 2, 3, 0, 2, 0, 3, 1

Offset: 1

Author

Gus Wiseman, Oct 14 2019

Keywords

• nonn

Comments

The nontrivial divisors of n are row n of A163870.

Examples

			The nontrivial divisors of 272 are {2, 4, 8, 16, 17, 34, 68, 136} with divisibility chains {{2, 4, 8, 16}, {17, 34, 68, 136}}, so a(272) = 4.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Positions of 1's are A328028 without 1.

The version with all divisors allowed is A328162.

Allowing n as a divisor of n gives A328195.

Indices of terms greater than 1 are A328189.

The maximum run-length of divisors of n is A055874(n).

Cf. A000005, A033676, A060775, A163870, A328026, A328161, A328171.

Programs

Mathematica

Table[Switch[n,1,0,?PrimeQ,0,,Max@@Length/@Split[DeleteCases[Divisors[n],1|n],Divisible[#2,#1]&]],{n,100}]

PARI

A328194(n) = if(1==n || isprime(n), 0, my(divs=divisors(n), rl=0,ml=1); for(i=2,#divs-1,if(!(divs[i]%divs[i-1]), rl++, ml = max(rl,ml); rl=1)); max(ml,rl)); \\ Antti Karttunen, Dec 07 2024

Extensions

Data section extended up to a(105) by Antti Karttunen, Dec 07 2024